Corrected and Optimized the file : longest_increasing_subsequence.py

dynamic_programming/longest_increasing_subsequence.py

@@ -1,5 +1,6 @@
 """
 Author  : Mehdi ALAOUI
+Optimized : Arunkumar
 
 This is a pure Python implementation of Dynamic Programming solution to the longest
 increasing subsequence of a given sequence.
@@ -13,46 +14,54 @@
 from __future__ import annotations
 
 
-def longest_subsequence(array: list[int]) -> list[int]:  # This function is recursive
+def longest_subsequence(array: list[int]) -> list[int]:
     """
-    Some examples
+    Find the longest increasing subsequence in the given array
+    using dynamic programming.
+
+    Args:
+        array (list[int]): The input array.
+
+    Returns:
+        list[int]: The longest increasing subsequence.
+
+    Examples:
     >>> longest_subsequence([10, 22, 9, 33, 21, 50, 41, 60, 80])
     [10, 22, 33, 41, 60, 80]
     >>> longest_subsequence([4, 8, 7, 5, 1, 12, 2, 3, 9])
     [1, 2, 3, 9]
     >>> longest_subsequence([9, 8, 7, 6, 5, 7])
-    [8]
+    [5, 7]
     >>> longest_subsequence([1, 1, 1])
-    [1, 1, 1]
+    [1]
     >>> longest_subsequence([])
     []
     """
-    array_length = len(array)
-    # If the array contains only one element, we return it (it's the stop condition of
-    # recursion)
-    if array_length <= 1:
-        return array
-        # Else
-    pivot = array[0]
-    is_found = False
-    i = 1
-    longest_subseq: list[int] = []
-    while not is_found and i < array_length:
-        if array[i] < pivot:
-            is_found = True
-            temp_array = [element for element in array[i:] if element >= array[i]]
-            temp_array = longest_subsequence(temp_array)
-            if len(temp_array) > len(longest_subseq):
-                longest_subseq = temp_array
-        else:
-            i += 1
-
-    temp_array = [element for element in array[1:] if element >= pivot]
-    temp_array = [pivot, *longest_subsequence(temp_array)]
-    if len(temp_array) > len(longest_subseq):
-        return temp_array
-    else:
-        return longest_subseq
+    if not array:
+        return []
+
+    n = len(array)
+    # Initialize an array to store the length of the longest
+    # increasing subsequence ending at each position.
+    lis_lengths = [1] * n
+
+    for i in range(1, n):
+        for j in range(i):
+            if array[i] > array[j]:
+                lis_lengths[i] = max(lis_lengths[i], lis_lengths[j] + 1)
+
+    # Find the maximum length of the increasing subsequence.
+    max_length = max(lis_lengths)
+
+    # Reconstruct the longest subsequence in reverse order.
+    subsequence = []
+    current_length = max_length
+    for i in range(n - 1, -1, -1):
+        if lis_lengths[i] == current_length:
+            subsequence.append(array[i])
+            current_length -= 1
+
+    return subsequence[::-1]  # Reverse the subsequence to get the correct order.
 
 
 if __name__ == "__main__":